Find the derivative of the following function. y=2^(-5x^(4)) Answer: y^(')=

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Find the derivative of the following function.  y=2^(-5x^(4)) Answer:  y^(')=

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Identify components: Identify the components of the function y = 2^(-5x^(4)). The base of the exponent is a constant (2), and the exponent is a function of x (-5x^(4)).Apply chain rule: Apply the chain rule for derivatives. The chain rule states that the derivative of a composite function is the derivative of the outer function evaluated at the inner function times the derivative of the inner function.Derivative of outer function: The outer function is 2^u, where u is the inner function -5x^(4). The derivative of 2^u with respect to u is 2^u * ln(2), because the derivative of a^x with respect to x is a^x * ln(a).Derivative of inner function: The inner function u(x) is -5x^(4). The derivative of -5x^(4) with respect to x is -20x^(3), because the derivative of x^n with respect to x is n*x^(n-1).Combine derivatives using chain rule: Combine the derivatives of the outer and inner functions using the chain rule. y' = d/dx[2^(-5x^(4))] = (2^(-5x^(4)) * ln(2)) * (-20x^(3))Simplify the expression: Simplify the expression for the derivative. y' = -20x^(3) * 2^(-5x^(4)) * ln(2)

Find the derivative of the following function. $\newline$ $y=2^{-5 x^{4}}$ $\newline$ Answer: $y^{\prime}=$

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Find the derivative of the following function.\newliney=2−5x4 y=2^{-5 x^{4}} y=2−5x4\newlineAnswer: y′= y^{\prime}= y′=

Find the derivative of the following function. $\newline$ $y=2^{-5 x^{4}}$ $\newline$ Answer: $y^{\prime}=$